## SAT SUBJECT TEST MATH LEVEL 1

## MISCELLANEOUS TOPICS

**CHAPTER 19**

**Logic**

• Statements

• Negations

• Conditional Statements

• Exercises

• Answers Explained

**T**hroughout the United States, math curricula vary considerably. Mathematical logic is taught in some schools but not in many others. On the Math 1 test, there should be at most one question involving mathematical logic. If you have studied logic in school, you have learned much more logic than you need for this test. If you review the few facts presented in this short section, you should have no problem with any logic question that may be on your Math 1 test.

If you never studied logic in school, don’t worry. If you carefully read the small amount of material in this section, and if you happen to encounter a logic question on your Math 1 test, you should be able to handle it without a problem.

**STATEMENTS**

In logic, a ** statement** is a sentence for which it is meaningful to say that it is true or false. In logic, statements are usually referred to by letters such as

*p*,

*q*, and

*r*. These letters will not appear on the Math 1 test, but using them here will simplify our discussion. Here are three statements:

*p*: 2 + 2 = 4*q*: Every prime number is odd.*r* : There is a real number *x* such that *x*^{2} + 1 = 0.

Note that statement *p* is true and that statements *q* and *r* are false.